What is the integral of ln(3/x) ?

The integral of ln(3/x) is xln(3/x)+x+C

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integral of ln(3/x)

\int ln (\frac{3}{x}) d x

x ln (\frac{3}{x}) + x + C

Solution steps

\int ln (\frac{3}{x}) d x

Apply Integration By Parts

: x ln (\frac{3}{x}) - \int - 1 d x

= x ln (\frac{3}{x}) - \int - 1 d x

\int - 1 d x = - x

= x ln (\frac{3}{x}) - (- x)

Simplify

= x ln (\frac{3}{x}) + x

Add a constant to the solution

= x ln (\frac{3}{x}) + x + C

\int - \frac{2}{( x + 1 ) ^{2}} d x

f (x) = ln (ln (ln (x)))

\frac{\partial}{\partial x} (x^{2} y cos (x y))

n = 0 \sum \infty \frac{n !}{10 0 ^{n}}

\frac{d y}{d x} = 15 x y